TESTING/EIG/ssvdct.f(3)

📦
version 3.12.1 · 2 versions
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🌸 NAME 🌸

Hi bestie!! This is the <pink>Library Functions Manual</pink> page for TESTING/EIG/ssvdct.f(3) — yep, TESTING/EIG/ssvdct.f — and it's literally all about the ssvdct subroutine. 💅✨

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

  • subroutine ssvdct (n, s, e, shift, num) — SSVDCT 👑

💖 Function/Subroutine Documentation 💖

🌈 subroutine ssvdct 🌈

subroutine ssvdct (integer n, real, dimension( * ) s, real, dimension( * ) e, real shift, integer num)

👑 SSVDCT 👑

🦋 Purpose 🦋

Okay so SSVDCT counts <purple>NUM</purple>, the number of eigenvalues of a 2*N by 2*N tridiagonal matrix T that are less than or equal to SHIFT — iconic behavior, no cap. 💖 T is formed by putting zeros on the diagonal and making the off-diagonals equal to S(1), E(1), S(2), E(2), ... , E(N-1), S(N).

If SHIFT is positive, NUM is equal to N plus the number of singular values of a bidiagonal matrix B less than or equal to SHIFT. In that setup, B has diagonal entries S(1), ..., S(N) and superdiagonal entries E(1), ... E(N-1). If SHIFT is negative, NUM is equal to the number of singular values of B greater than or equal to -SHIFT. 🌈

And the reference is right here: W. Kahan , Report CS41, Computer Science Dept., Stanford University, July 21, 1966. 📚✨

🍓 Parameters 🍓

  • N — N is INTEGER; it's the dimension of the bidiagonal matrix B. 🎀
  • S — S is REAL array, dimension (N); these are the diagonal entries of the bidiagonal matrix B. 🍓
  • E — E is REAL array of dimension (N-1); these are the superdiagonal entries of the bidiagonal matrix B. 🦋
  • SHIFT — SHIFT is REAL; it's the shift, used as described under Purpose. 💫
  • NUM — NUM is INTEGER; it's the number of eigenvalues of T less than or equal to SHIFT. 👑

🫶 Author 🫶

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

📍 Definition at line 86 of file ssvdct.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code. 🤖💖

mwah 💋 — that's the whole page for LAPACK Version 3.12.0, TESTING/EIG/ssvdct.f(3). Byeee bestie, go count those eigenvalues 🫶✨

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